The opener clobbered 16 sixes, the joint-most in an innings in men's T20 Internationals, to power New Zealand to an imposing 224-7 at the University Oval.
Pakistan managed 179-7 in reply, including Babar Azam's (58) third fifty of the series, as New Zealand took an unassailable 3-0 lead in the five-match series.
Allen toyed with the entire Pakistan attack but was particularly harsh on Haris Rauf, plundering 28 runs, including three sixes, in the fast bowler's second over, taking him out of the attack.
The bowler was brought back in after New Zealand cruised to 109-1 at the halfway stage and Allen smacked three sixes in that over from Rauf, who bled 60 runs for his two wickets.
Babar kept Pakistan in the hunt for a while but Tim Southee (2-29) led New Zealand's disciplined bowling to ensure they were never really threatened.
"It's good to see the hard work of the last few months come off," Player of the Match Allen said of his knock, which also included five fours.
"I'm not so personal milestone-driven. I suppose it's just good to get across the line and put up a competitive score and take the series."
This is Pakistan's first series under new T20 captain Shaheen Afridi ahead of this year's 20-overs World Cup in June.
The last two matches of the series are scheduled in Christchurch on Friday and Sunday.
